Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We define a class of measures having the following properties:
(1) the measures are supported on self-similar fractal subsets of the unit cube $I^{M} = [0,1)^{M}$, with 0 and 1 identified as necessary;
(2) the measures are singular with respect to normalized Lebesgue measure m on $I^{M}$;
(3) the measures have the convolution property that $μ∗ L^{p} ⊆ L^{p+ε}$ for some ε = ε(p) > 0 and all p ∈ (1,∞).
We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then $μ ∗ L^{p} ⊆ L^{q}$ for any measure μ in our class.
(1) the measures are supported on self-similar fractal subsets of the unit cube $I^{M} = [0,1)^{M}$, with 0 and 1 identified as necessary;
(2) the measures are singular with respect to normalized Lebesgue measure m on $I^{M}$;
(3) the measures have the convolution property that $μ∗ L^{p} ⊆ L^{p+ε}$ for some ε = ε(p) > 0 and all p ∈ (1,∞).
We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then $μ ∗ L^{p} ⊆ L^{q}$ for any measure μ in our class.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
171-177
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- Department of Mathematics, Stetson University, P.O. Box 7532, Daytona Beach, FL 32116, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-1